Given #Sec θ=9#, what are the other trig functions given tanθ<0?

1 Answer
Jul 29, 2016

Answer:

#costheta=1/9#
#sintheta=sqrt80/9#
#cosectheta=9/sqrt80#
#tantheta=sqrt80#
#cottheta=1/sqrt80#

Explanation:

#sectheta=9#
#costheta=1/sectheta=1/9#=======Ans #1#

#sintheta=sqrt(1-cos^2theta)#
or
#sintheta=sqrt(1-(1/9)^2#
or
#sintheta=sqrt(1-1/81#
or
#sintheta=sqrt((81-1)/81)#
or
#sintheta=sqrt(80/81)#
or
#sintheta=sqrt80/9#==========Ans #2#
#cosectheta=1/sintheta=9/sqrt80#=========Ans #3#
#tantheta=sintheta/costheta=sqrt(80)/9-:(1/9)=sqrt80#=======Ans #4#

#cottheta=1/tantheta=1/sqrt80#==========Ans #5#